Instantons in Self-Organizing Logic Gates

Self-organizing logic [1] is a recently-suggested framework that allows the solution of Boolean truth tables “in reverse,” i.e., it is able to satisfy the logical proposition of gates regardless to which terminal(s) the truth value is assigned. It can be realized if time non-locality (memory) is present. By employing a practical realization of such gates using electronic circuits with memory, we show, numerically, that SOLGs exploit elementary instantons to reach equilibrium points [2]. Instantons are classical trajectories of the non-linear equations of motion describing SOLGs that connect topologically distinct critical points in the phase space. Our work provides a physical understanding of, and can serve as an inspiration for, new models of bi-directional logic gates that are emerging as important tools in physics-inspired, unconventional computing.
[1] F. L. Traversa and M. Di Ventra, Chaos: An Interdisciplinary Journal of Nonlinear Science 27, 023107, 2017
[2] S.R.B. Bearden, H. Manukian, F.L. Traversa, M. Di Ventra, arXiv:1708.08949